I am not warrantying how it will work, but if within the obarun pacman.conf you substitute hyperbola's instead of arch's mirrors it should work. You should also run pacopts origin to make sure pkgs with the same name do come from obarun and not hyperbola (like eudev libeudev may be incompatible, I don't know). Also hyperbola's pkgs are way behind arch, so there might be a case somewhere of incompatible library .. like too old of a glibc. But just for getting s6 and 66 to work, which are pretty autonomous and disregarding the rest of the system, I am pretty sure it will work.
Also everything in s6 and 66 is free but I don't think they have fsf certification ...
After you get obarun repositories on, turn SigLevel = Never install the obarun-keyring and pacman, run pacman-key --populate obarun hyperbola to make sure it is ok then revert the value or move pacman.conf.pacnew to its right place pacman.conf and replace the arch with hyperbola repositories. Then install s6-suite which incorporates s6 and 66 .

I don't know if there will be a conlfict with openrc, there might be some init-rc pkg that will create conflict (init, shutdown, reboot, poweroff, halt) but if you can rename those out of the way and let s6-suite install clean openrc can remain installed and be out of the way. Like MX has systemd installed and not used.

it could be better to build the necessary on your system, hyperbola may use different package policies directories installation and different options support for the binary.
Simply grab the pkgbuild from here and build it on your host. You need: skalibs,execline,s6,s6-rc,s6-linux-utils,s6-portable-utils,oblibs,66 and 66-tools. Build it in that order.
Than you can need: boot-66serv, tty@ -66serv to be able to boot your machine and some other from here